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Shape memory polymers are gaining significant interest as one of the major constituent materials for the emerging field of 4D printing. While 3D-printed metamaterials with shape memory polymers show unique thermomechanical behaviors, their thermal transport properties have received relatively little attention. Here, we show that thermal transport in 3D-printed shape memory polymers strongly depends on the shape, solid volume fraction, and temperature and that thermal radiation plays a critical role. Our infrared thermography measurements reveal thermal transport mechanisms of shape memory polymers in varying shapes from bulk to octet-truss and Kelvin-foam microlattices with volume fractions of 4%–7% and over a temperature range of 30–130 °C. The thermal conductivity of bulk shape memory polymers increases from 0.24 to 0.31 W m −1  K −1 around the glass transition temperature, in which the primary mechanism is the phase-dependent change in thermal conduction. On the contrary, thermal radiation dominates heat transfer in microlattices and its contribution to the Kelvin-foam structure ranges from 68% to 83% and to the octet-truss structure ranges from 59% to 76% over the same temperature range. We attribute this significant role of thermal radiation to the unique combination of a high infrared emissivity and a high surface-to-volume ratio in the shape memory polymer microlattices. Our work also presents an effective medium approach to explain the experimental results and model thermal transport properties with varying shapes, volume fractions, and temperatures. These findings provide new insights into understanding thermal transport mechanisms in 4D-printed shape memory polymers and exploring the design space of thermomechanical metamaterials.